A tentative Replica Study of the Glass Transition

Abstract

We propose a method to study quantitatively the glass transition in a system of interacting particles. In spite of the absence of any quenched disorder, we introduce a replicated version of the hypernetted chain equations. The solution of these equations, for hard or soft spheres, signals a transition to the glass phase. However the predicted value of the energy and specific heat in the glass phase are wrong, calling for an improvement of this method.

9 pages, four postcript figures attached

References in corpus (7)

• The structural glass transition and the entropy of the metastable states
• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Recipes for metastable states in Spin Glasses
• Dynamics within metastable states in a mean-field spin glass
• $D$-dimensional Arrays of Josephson Junctions, Spin Glasses and $q$-deformed Harmonic Oscillators
• A mean-field hard-spheres model of glass
• Slow Dynamics in Glasses

Cited by in corpus (57)

• Supercooled Liquids for Pedestrians
• Fractal free energy landscapes in structural glasses
• Thermodynamics of glasses: a first principle computation
• Phase diagram of glassy systems in an external field
• On nonlinear susceptibility in supercooled liquids
• Ehrenfest relations at the glass transition: solution to an old paradox
• Modern computational studies of the glass transition
• Constrained Boltzmann-Gibbs measures and effective potential for glasses in hypernetted chain approximation and numerical simulations
• Effective potential in glassy systems: theory and simulations
• Microscopic theory of the jamming transition of harmonic spheres
• Dynamic Glass Transition in Two Dimensions
• Glass transition and effective potential in the hypernetted chain approximation
• How to compute the thermodynamics of a glass using a cloned liquid
• Glass transition of hard spheres in high dimensions
• Dynamical transition of glasses: from exact to approximate
• Toy model for the mean-field theory of hard-sphere liquids
• Quantitative field theory of the glass transition
• The shear modulus of glasses: results from the full replica symmetry breaking solution
• Phase Behavior of Type-II Superconductors with Quenched Point Pinning Disorder: A Phenomenological Proposal
• Self-induced spin glass state in elemental and crystalline neodymium
• Quantitative approximation schemes for glasses
• Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach
• Statics and dynamics of infinite-dimensional liquids and glasses: a parallel, compact derivation
• Static replica approach to critical correlations in glassy systems
• Time scale separation and heterogeneous off-equilibrium dynamics in spin models over random graphs
• A thermodynamic description of colloidal glasses
• Mode-coupling theory for multiple decay channels
• Energy landscape - a key concept for the dynamics of glasses and liquids
• Mean field stability map of hard-sphere glasses
• Mean-field caging in a random Lorentz gas
• Dynamical critical exponents for the mean-field Potts glass
• Phase Diagram of a Classical Fluid in a Quenched Random Potential
• Microscopic theory for the glass transition in a system without static correlations
• Systematic expansion in the order parameter for replica theory of the dynamical glass transition
• Self-induced glassiness and pattern formation in spin systems subject to long-range interactions
• On the overlap between configurations in glassy liquids
• Manifestation of Random First Order Transition theory in Wigner glasses
• Quasi-equilibrium in glassy dynamics: a liquid theory approach
• Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects
• Brownian dynamics: from glassy to trivial
• Phase Diagram Of A Hard-sphere System In A Quenched Random Potential: A Numerical Study
• Glass transition in systems without static correlations: a microscopic theory
• Dynamical arrest and replica symmetry breaking in attractive colloids
• A tentative replica theory of glassy Helium 4
• Can the jamming transition be described using equilibrium statistical mechanics?
• Theory of simple glasses
• Quasi equilibrium construction for the long time limit of glassy dynamics
• Quantitative investigation of the mean-field scenario for the structural glass transition from a schematic mode-coupling analysis of experimental data
• Statistical Mechanics of a Two-Dimensional System with Long Range Interaction
• Packing hard spheres with short-range attraction in infinite dimension: Phase structure and algorithmic implications
• How to break the replica symmetry in structural glasses
• Integral-equation analysis of single-site coarse-grained models for polymer-colloid mixtures
• Metastable states in the Blume-Emery-Griffiths spin glass model
• Logarithmic critical slowing down in complex systems: from statics to dynamics
• Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
• Glass and jamming transition of simple liquids: static and dynamic theory
• An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids